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Coordinate Geometry (15%). Questions in this content are based on graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves; graphing inequalities; slope; parallel and perpendicular lines; distance; midpoints; and conics.

坐标几何（ 15 ％）。这方面的考试内容是基于方程和图表之间的关系，包括点，线，多项式，圆形和其它的曲线图；不相等图形；斜率；平行和垂直线；距离；中点；以及二次曲线。

Many subdivision schemes have been proposed in the recent three decades, however, most of them are not capable of both reproducing families of curves widely used in Computer Graphics such as conics, and controlling the shape of the limit curve by a tension parameter.

近三十年来已有多种细分方法被相继提出，然而大多数细分方法不能既生成在计算机图形学中广泛应用的特殊曲线，例如圆弧曲线，又存在一个松弛参数能够调整极限曲线的形状。

The parallel-connection and variable-speed operation characters of the centrifugal pump groups are studied by conics fitting of the character curves in the high efficiency area.

通过对离心式水泵高效工作区的性能曲线进行二次拟合，分析了离心式水泵机组并联调速运行特性。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

According to theory of the conjugate curves and the envelope curve,the corresponding mathematic model of workpiece-tooth-curve was established.

并根据共轭曲线及包络线理论建立对应工件齿廓曲线的数模型，由二者的数学模型建立完全接触面积的算法。

Firstly, the characteristic points of the parallel section curves are extracted, and the characteristic points are connected to construct feature curve.

然后在上述区域划分的基础上，提出结合树形结构利用数据点的法矢量对区域内数据点群完成空间分割，从而形成具有单一表面特征的面片。

The structure feature of the sensor was described in comparison with the classical Stewart platform-based six-component force sensor.By using the finite element method,the elastic dynamics theoretical model of the sensor was established based on the conditions of displacement consistency and force balance.According to this model,the numerical analysis was carried out,and the variety relationship curves between the natural frequencies and the structural parameters are plotted.

描述了该传感器相对于经典Stewart平台六维力传感器所具有的结构特点；利用有限元法，采用位移协调和力平衡条件建立了传感器弹性动力学理论模型，依此模型进行数值分析，绘制了固有频率与各结构参数间变化关系曲线；并利用ANSYS软件建立了传感器有限元模型，进行了振动模态分析，得到其固有频率和振型。

Time are tested under different kinds of stress for nitrided and un-nitrided specimens made from 35CrMo steel. The testing time ranges from 70 to 80 hours. The following equations are regressed from the tested curves: Un-nitrided specimens:〓 Nitrided specimens:〓 The above equations are consistent with the first stage theory for creep.

为此本文通过实验，测试了35CrMo钢渗氮和未渗氮两种试样在500℃时不同应力情况下的应变随时间的变化曲线，实验时间为70-80小时，将测得的曲线回归出以下方程：未渗氮样品：〓渗氮样品：〓以上方程符合蠕变的第一阶段陈化理论公式。

These curves are consistent with test data and the results suggest that the procedure proposed in this work is valid.

这个数值算例表明本文提出的方法是行之有效的。

A consumer's preference among consumption bundles may be illustrated with indifference curves.

在一束消费品当中，消费者的偏好可以用无差异曲线来说明。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。